Discard loose fat from rabbit. Rinse & pat dry. In a large bowl combine carrot, garlic, bay leaves, allspice, pepper, 1 Tbls. Oil, wine, orange juice, orange rind, & rum. Add the rabbit. Chill, covered, turning occasionally, for 24 hours. Remove rabbit from the bowl, reserving the marinade, & pat dry. In a large skillet heat the remaining 2 Tbls. Olive oil & brown the rabbit. Sprinkle with 1 Tbls. Flour, turn it, & brown the flour. Repeat with the remaining 1 Tbls. Flour. Transfer the rabbit to a large casserole. Salt to taste.
Deglaze the skillet with the reserved marinade. Pour over the rabbit. Cook, covered at 350 for 1-1 1/2 hours, basting twice, till very tender. Transfer to a heated platter, pour sauce over it, & garnish with sliced orange.